- #1
mateomy
- 307
- 0
Practicing the derivations of the Motion Equations, and I am looking through my notes that I transcribed from my professor...Im getting caught up on one spot.
Im getting all the equations to "pop out" except for this last one, which, I can see; but, the algebra is throwing me off...
Finishing off with these as the fundamentals to get the last derivation:
[tex]
x=v_0 + at ; t= \frac{v-v_0}{a} ; x=x_0 + v_0 t + \frac{1}{2}at^2
[/tex]
Substituting the new t value into the latter equation and expanding...
[tex]
x= x_0 + \frac{v_0 v}{a} - \frac{v_0^2}{a} + \frac{v^2}{2a} - \frac{v_0^2}{2a} - \frac{v_0 v}{a}
[/tex]
I can't seem to get the fractions to add and subtract out in the right way so that I can get the final equation of
[tex]
x= x_0 + \frac{1}{2a}(v^2 - v_0^2)
[/tex]
Specifically I can't get the -v(initial)^2/a and the -v(initial)^2/2a to add up so that I can factor (in the final equation) out the 1/2. I know I am doing something absent minded. Can somebody please point it out? Thank you in advance for any pointers.
Im getting all the equations to "pop out" except for this last one, which, I can see; but, the algebra is throwing me off...
Finishing off with these as the fundamentals to get the last derivation:
[tex]
x=v_0 + at ; t= \frac{v-v_0}{a} ; x=x_0 + v_0 t + \frac{1}{2}at^2
[/tex]
Substituting the new t value into the latter equation and expanding...
[tex]
x= x_0 + \frac{v_0 v}{a} - \frac{v_0^2}{a} + \frac{v^2}{2a} - \frac{v_0^2}{2a} - \frac{v_0 v}{a}
[/tex]
I can't seem to get the fractions to add and subtract out in the right way so that I can get the final equation of
[tex]
x= x_0 + \frac{1}{2a}(v^2 - v_0^2)
[/tex]
Specifically I can't get the -v(initial)^2/a and the -v(initial)^2/2a to add up so that I can factor (in the final equation) out the 1/2. I know I am doing something absent minded. Can somebody please point it out? Thank you in advance for any pointers.